The Mountain Hawks (20-8, 10-4) led 53-37 with 13:04 remaining, but the Black Knights (15-14, 8-6) used a 25-9 run to tie it at 62, getting eight points each from Ella Ellis and Kyle Wilson.
Lehigh went back in front on Justin Goldsborough's free throw and pulled out to a seven-point lead, 75-68, with 1:05 remaining after Greiner ran off two baskets and two free throws.
Ellis finished with 30 points for Army, which had won five straight. The senior has scored 30 or more points three times in his last four games and is now fifth on Army's career scoring list with 1,558 points.
Both teams will host first-round tournament games. Lehigh will play Colgate and fourth-seeded Army will host American University.